1. Field of the Invention
The present invention relates to a method for optimizing parameters related to control processing by a control system. More particularly, the present invention relates to a parameter optimization method that is suitable for optimizing parameters in real time.
2. Description of the Related Art
Response surface methodology (RSM) has been well known as a technique for quickly determining a suboptimal solution to a parameter related to control processing by a control system for a marine vessel (“marine vessel” refers to a ship or a boat), automobile, or the like. The response surface methodology involves creating a statistical model called a response surface from sample values and performing optimization on the response surface. This methodology is useful when a gradient method cannot be used because a function to be optimized is not continuous or when simulations involve very high computational costs. Particular examples of this methodology, the Monte Carlo method and experimental design, are often used to obtain sample values efficiently (see Non-patent Literature 1).
Also, a technique has been proposed which involves collecting sample values around an optimum value estimated from an obtained response surface, creating a new response surface using the sample values, and thereby improving accuracy gradually. Since this technique creates a rough response surface initially and improves accuracy gradually by using sample values around the estimated optimum value, it can obtain a suboptimal solution quickly using a small number of samples.
For example, a technique called a sequential approximate optimization (SAO) (see Non-patent Literature 2) performs optimization in small regions called sub-regions using small-quantity sampling and response surfaces based on an experimental design, calculates accuracy from an estimated value obtained from a response surface of the optimized solution and an actual evaluated value, and obtains an optimum solution by repeating moves, contractions, and expansions of sub-regions according to the accuracy. Also, a technique which incorporates crossover used in real-coded genetic algorithms has been proposed for efficient sampling around an optimum solution (see Non-patent Literature 3 described below).
Generally, the response surface methodology and its modifications are recognized as techniques for optimizing large-scale simulations and real systems off-line, but they are also considered to be effective in optimizing real systems on-line in a short time.
In the following description, Non-patent Literature 1 refers to Todoroki: Introduction to Optimum Design of Nonlinear Problems Using Response Surface Methodology, material for a workshop of The Japan Society of Mechanical Engineers (1999); Non-patent Literature 2 refers to Guinta and Eldred: Implementation of a Trust Region Model Management Strategy in the DAKOTA Optimization Toolkit, paper AIAA-2000-4935 in Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, Sep. 6-8 (2000); and Non-patent Literature 3, refers to Hasegawa, et al., A Simulation on Sequential Approximate Optimization-Based Real-type Crossover Model and Response Surface Model, Transactions of The Japan Society for Computational Engineering and Science, No. 20000019 (2000).
The techniques proposed so far, when used for on-line optimization of real systems, poses such problems as variation of sample values and deviation of an estimated solution due to a positional relationship between a sampling range and an optimum solution.
Regarding the variation of sample values, there is no need to take it into consideration in the case of simulations. When optimizing actual devices off-line, it is possible to create an experimental environment which enables stable measurements by minimizing observation errors.
However, when performing on-line optimization in a real environment, it is difficult to take stable measurements because of subtle variations in system operation caused by uncontrollable factors as well as because of noise added to measuring instruments. This results in a large variation of sample values with respect to the shape of a function to be optimized, adversely affecting the accuracy of response surfaces. In particular, failure of the system to operate properly due to an unexpected disturbance will produce outliers, which are known to adversely affect the creation of response surfaces by the least squares method.
Now, the deviation of an estimated solution due to the positional relationship between the sampling range and the optimum solution will be described. If sample values are collected with a parameter that is varied greatly when the system is actually operating, the system behavior may be changed greatly. In particular, if the system is used by people (e.g., a vehicle), this type of sampling is impossible. In such a case, an effective way is to start initial sampling in a small range in which somewhat stable operation is known to be available and estimate an optimum solution by increasing the sampling range gradually.
However, if a large noise is added to sample values and an optimum solution exists outside an initial sampling range, an estimated optimum solution is biased by the initial sampling range, making it impossible to obtain the true optimum solution.
This is because sample values collected near boundaries of the sampling range affect the shape of the response surface greatly. This can be seen, for example, from the fact that when impact of each sample value on the response surface is checked using Cook's distance in regression diagnostics given by Equation (1) below, the sample values near the boundaries have greater impact than those around the center.
                    Formula        ⁢                                  ⁢        1                                                                                  Cook            '                    ⁢          s          ⁢                                          ⁢          Distance                =                              ∑                          j              =              1                        n                    ⁢                                                    (                                                      yhat                    ji                                    -                                      yhat                    j                                                  )                            2                        /                          (                                                p                  ·                  σ                                ⁢                                                                  ⁢                                  hat                  2                                            )                                                          (        1        )            where yhatj is an estimated value of a response surface created using all the samples, yhatji is an estimated value of a response surface created using all the samples except the i-th sample, p is the number of parameters in the model, and σhat2 is an estimated value of variance.
When an optimum value exists outside the initial sampling range, if sample values near the boundaries are far larger or far smaller than they should be due to the influence of noise, estimation accuracy of the optimum value will degrade greatly, which will have a fatal impact in on-line optimization in which the number of times of sampling is limited.
Thus, the response surface methodology and its modifications proposed conventionally cannot deal with the above-described problems for the reasons described above if final details of the system are undecided in the design phase although they are useful as an optimization technique for use before shipment.
Specifically, for example, it is difficult to predict before shipment what combination of an outboard device and hull the user will select and if the user intends to perform constant-speed navigation control or attitude angle control in a desired hull, it will become necessary to optimize system parameters after shipment. When using the Monte Carlo method or experimental design to obtain sample values for optimization, a problem arises as to how to set adjustable parameter ranges in which sample values are collected. If the ranges are too small, the true optimum solution cannot be obtained for the reasons described above and if they are too large, sharp changes may occur in the operation of the system, causing the system to behave unexpectedly. Also, since the weight and center of gravity of a system consisting of an outboard device and hull change greatly depending on the number of people aboard the marine vessel as well as on cargo, it is not true that once the system is optimized, it is always ready for operation, but the system must be optimized continuously.